Problem 95 - Chemistry Matter and Change

Question

How many moles contain the given quantity? a. \(1.25 \times 10^{15}\) molecules of carbon dioxide b. \(3.59 \times 10^{21}\) formula units of sodium nitrate c. \(2.89 \times 10^{27}\) formula units of calcium carbonate

Step-by-Step Solution

Answer

In summary, the given quantities contain: a. \(2.075 \times 10^{-9}\) moles of carbon dioxide b. \(5.963 \times 10^{-3}\) moles of sodium nitrate c. \(4.801 \times 10^3\) moles of calcium carbonate

Step 1: Calculate moles for carbon dioxide

Given quantity: \(1.25 \times 10^{15}\) molecules of CO₂ Avogadro's Number: \(6.022 \times 10^{23}\) Moles of CO₂ = \(\frac{1.25 \times 10^{15}}{6.022 \times 10^{23}}\) Moles of CO₂ = \(2.075 \times 10^{-9}\) moles

Step 2: Calculate moles for sodium nitrate

Given quantity: \(3.59 \times 10^{21}\) formula units of NaNO₃ Avogadro's Number: \(6.022 \times 10^{23}\) Moles of NaNO₃ = \(\frac{3.59 \times 10^{21}}{6.022 \times 10^{23}}\) Moles of NaNO₃ = \(5.963 \times 10^{-3}\) moles

Step 3: Calculate moles for calcium carbonate

Given quantity: \(2.89 \times 10^{27}\) formula units of CaCO₃ Avogadro's Number: \(6.022 \times 10^{23}\) Moles of CaCO₃ = \(\frac{2.89 \times 10^{27}}{6.022 \times 10^{23}}\) Moles of CaCO₃ = \(4.801 \times 10^3\) moles So, in summary: a. \(2.075 \times 10^{-9}\) moles of carbon dioxide b. \(5.963 \times 10^{-3}\) moles of sodium nitrate c. \(4.801 \times 10^3\) moles of calcium carbonate

Key Concepts

Avogadro's number

Avogadro's Number is one of the cornerstones of chemistry, especially when dealing with moles and molecular calculations. It is defined as the number of constituent particles (usually atoms, molecules, or ions) in one mole of a given substance. This number is approximately equal to \(6.022 \times 10^{23}\). When dealing with chemistry problems, Avogadro's Number allows us to convert between number of particles and moles, helping us understand the scale at which changes occur in chemical reactions. For example, if you have a specific quantity of molecules, as we do in the original exercise, using Avogadro's Number helps to determine how many moles those molecules represent.

• To find the number of moles, divide the number of molecules or formula units by Avogadro's Number.
• Always ensure that the number derived is in moles, as this is a more practical unit for reactions and stoichiometry.

carbon dioxide

Carbon Dioxide (CO₂) is a simple molecular compound with carbon and oxygen as its components. It is a well-known greenhouse gas. Understanding the concept of moles in the context of CO₂ means knowing how many molecules there are in a given mass.In the original step-by-step solution, you might notice that to find the moles of CO₂ given the molecules \(1.25 \times 10^{15}\), we use the formula: \[\text{Moles of } \text{CO}_2 = \frac{\text{Number of molecules}}{6.022 \times 10^{23}}\]Using this relationship helps us to calculate small quantities of substances that we would encounter in laboratories.

• CO₂ is a key focus in environmental chemistry.
• Calculating its moles can help in understanding its impact in different chemical processes.

sodium nitrate

Sodium Nitrate (NaNO₃) is an ionic compound with significant roles in industries such as fertilizers and food preservation. Its formula units are made up of sodium, nitrogen, and oxygen.The calculation of moles in sodium nitrate involves counting the number of formula units. In the example given, we have \(3.59 \times 10^{21}\) formula units. To convert this to moles, use Avogadro's Number as shown:\[\text{Moles of NaNO}_3 = \frac{3.59 \times 10^{21}}{6.022 \times 10^{23}}\]This helps chemists determine the amount of sodium nitrate involved in reactions or processes.

• Sodium nitrate's use can vary from explosives to food preservation.
• Knowing its molar value is crucial for chemical manufacturing applications.

calcium carbonate

Calcium Carbonate (CaCO₃) is a common compound in geology and biology. It's found in rocks like limestone and in the shells of marine organisms.When calculating moles for the compound, we first count its formula units. In our exercise, the given quantity is \(2.89 \times 10^{27}\) formula units. Using Avogadro's Number, these units are converted to moles:\[\text{Moles of CaCO}_3 = \frac{2.89 \times 10^{27}}{6.022 \times 10^{23}}\]This conversion is key in understanding the volume and weight of substances we deal with in chemistry.

• Calcium carbonate is crucial for constructing buildings and is a component in antacids.
• Knowing its molar quantity aids in industrial uses and scientific research.